矩形面积和矩形周长并的模板——来自notonlysuccess

矩形面积并

hdu1542 Atlantis

题意:矩形面积并
思路:浮点数先要离散化;然后把矩形分成两条边,上边和下边,对横轴建树,然后从下到上扫描上去,用cnt表示该区间下边比上边多几个,sum代表该区间内被覆盖的线段的长度总和
这里线段树的一个结点并非是线段的一个端点,而是该端点和下一个端点间的线段,所以题目中r+1,r-1的地方可以自己好好的琢磨一下
线段树操作:update:区间增减 query:直接取根节点的值

#include <cstdio>#include <cstring>#include <cctype>#include <algorithm>using namespace std;#define lson l , m , rt << 1#define rson m + 1 , r , rt << 1 | 1 const int maxn = 2222;int cnt[maxn << 2];double sum[maxn << 2];double X[maxn];struct Seg {double h , l , r;int s;Seg(){}Seg(double a,double b,double c,int d) : l(a) , r(b) , h(c) , s(d) {}bool operator < (const Seg &cmp) const {return h < cmp.h;}}ss[maxn];void PushUp(int rt,int l,int r) {if (cnt[rt]) sum[rt] = X[r+1] - X[l];else if (l == r) sum[rt] = 0;else sum[rt] = sum[rt<<1] + sum[rt<<1|1];}void update(int L,int R,int c,int l,int r,int rt) {if (L <= l && r <= R) {cnt[rt] += c;PushUp(rt , l , r);return ;}int m = (l + r) >> 1;if (L <= m) update(L , R , c , lson);if (m < R) update(L , R , c , rson);PushUp(rt , l , r);}int Bin(double key,int n,double X[]) {//离散化int l = 0 , r = n - 1;while (l <= r) {int m = (l + r) >> 1;if (X[m] == key) return m;if (X[m] < key) l = m + 1;else r = m - 1;}return -1;}int main() {int n , cas = 1;while (~scanf("%d",&n) && n) {int m = 0;while (n --) {double a , b , c , d;scanf("%lf%lf%lf%lf",&a,&b,&c,&d);//左上和右下X[m] = a;ss[m++] = Seg(a , c , b , 1);X[m] = c;ss[m++] = Seg(a , c , d , -1);}sort(X , X + m);sort(ss , ss + m);int k = 1;for (int i = 1 ; i < m ; i ++) {if (X[i] != X[i-1]) X[k++] = X[i];}memset(cnt , 0 , sizeof(cnt));memset(sum , 0 , sizeof(sum));double ret = 0;for (int i = 0 ; i < m - 1 ; i ++) {int l = Bin(ss[i].l , k , X);int r = Bin(ss[i].r , k , X) - 1;if (l <= r) update(l , r , ss[i].s , 0 , k - 1, 1);ret += sum[1] * (ss[i+1].h - ss[i].h);}printf("Test case #%d\nTotal explored area: %.2lf\n\n",cas++ , ret);}return 0;}

矩形周长并

hdu1828 Picture

题意:矩形周长并
思路:与面积不同的地方是还要记录竖的边有几个(numseg记录),并且当边界重合的时候需要合并(用lbd和rbd表示边界来辅助)
线段树操作:update:区间增减 query:直接取根节点的值

#include <cstdio>#include <cstring>#include <cctype>#include <algorithm>using namespace std;#define lson l , m , rt << 1#define rson m + 1 , r , rt << 1 | 1 const int maxn = 22222;struct Seg{int l , r , h , s;Seg() {}Seg(int a,int b,int c,int d):l(a) , r(b) , h(c) , s(d) {}bool operator < (const Seg &cmp) const {if (h == cmp.h) return s > cmp.s;return h < cmp.h;}}ss[maxn];bool lbd[maxn<<2] , rbd[maxn<<2];int numseg[maxn<<2];int cnt[maxn<<2];int len[maxn<<2];void PushUP(int rt,int l,int r) {if (cnt[rt]) {lbd[rt] = rbd[rt] = 1;len[rt] = r - l + 1;numseg[rt] = 2;} else if (l == r) {len[rt] = numseg[rt] = lbd[rt] = rbd[rt] = 0;} else {lbd[rt] = lbd[rt<<1];rbd[rt] = rbd[rt<<1|1];len[rt] = len[rt<<1] + len[rt<<1|1];numseg[rt] = numseg[rt<<1] + numseg[rt<<1|1];if (lbd[rt<<1|1] && rbd[rt<<1]) numseg[rt] -= 2;//两条线重合}}void update(int L,int R,int c,int l,int r,int rt) {if (L <= l && r <= R) {cnt[rt] += c;PushUP(rt , l , r);return ;}int m = (l + r) >> 1;if (L <= m) update(L , R , c , lson);if (m < R) update(L , R , c , rson);PushUP(rt , l , r);}int main() {int n;while (~scanf("%d",&n)) {int m = 0;int lbd = 10000, rbd = -10000;for (int i = 0 ; i < n ; i ++) {int a , b , c , d;scanf("%d%d%d%d",&a,&b,&c,&d);//左下和右上lbd = min(lbd , a);rbd = max(rbd , c);ss[m++] = Seg(a , c , b , 1);ss[m++] = Seg(a , c , d , -1);}sort(ss , ss + m);int ret = 0 , last = 0;for (int i = 0 ; i < m ; i ++) {if (ss[i].l < ss[i].r) update(ss[i].l , ss[i].r - 1 , ss[i].s , lbd , rbd - 1 , 1);ret += numseg[1] * (ss[i+1].h - ss[i].h);ret += abs(len[1] - last);last = len[1];}printf("%d\n",ret);}return 0;}